Characterisation of ttH production at 13 TeV in the multijet topologies with CMS

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Alma Mater Studiorum · Università di Bologna

SCUOLA DI SCIENZE Dipartimento di Fisica e Astronomia Corso di Laurea Magistrale in Fisica

Characterisation of t¯tH production

at 13 TeV in the multijet topologies

with CMS

Relatore:

Prof. Andrea Castro

Eric Ballabene

Presentata da:

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III

Abstract

The associated production of a top quark pair with a Higgs boson (t¯tH) is very important because, in spite of its small production cross section, it enables the direct measurement of the Yukawa coupling of the Higgs boson to the top quark. The final states of t¯tH events depend on the specific decay of the top quarks and of the Higgs boson, and different topologies are originated, with or without energetic leptons in the final states. The events studied in this work correspond to an all-jet topology, with some of these jets which might be subject to boost given the large transverse momentum involved. It is therefore essential to classify the final states in terms of the number of “resolved” and “boosted” jets, and for each case different triggers are required. Since the background yields (mainly from top quark-antiquark pairs and QCD multijet production) are much larger than the expected signal, special care needs to be used to reduce them. The event selection is based on multivariate analysis algorithms which can distinguish signal from background events, and boosted jets associated to top quarks, to the Higgs bosons or to generic light quarks, enabling the definition of different event categories. The statistical performance of this analysis is characterised by two essential parameters, the upper limits on the signal strength and the signal significance. The expected upper limits on the signal strength are estimated at 95% confidence level, along with the signal significance, for each category and for the combination of all categories.

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V

Sommario

La produzione associata di una coppia di quark top con un bosone di Higgs (t¯tH) è molto importante perché, nonostante la sua piccola sezione d’urto di produzione, permette la misura diretta dell’accoppiamento di Yukawa del bosone di Higgs con il quark top. Gli stati finali degli eventi t¯tH dipendono dallo specifico decadimento dei quark top e del bosone di Higgs e differenti topologie possono essere originate, con o senza leptoni ener-getici negli stati finali. Gli eventi studiati in questo lavoro corrispondono alla topologia all-jet, con alcuni di questi jet che possono essere soggetti a boost dato l’elevato momento trasverso in gioco. È pertanto essenziale classificare gli stati finali in termini del numero di jet risolti o soggetti a boost, e per ciascun caso diversi trigger sono richiesti. Dal mo-mento che il contributo di fondo (principalmente dalla produzione di coppie del quark top e dal fondo QCD multijet) è molto più grande del segnale atteso, particolare attenzione deve essere usata per ridurlo. La selezione degli eventi è basata su algoritmi di analisi multivariata che possono distinguere eventi di segnale dal fondo, e jet associati ai quark top, ai bosoni di Higgs o a generici quark leggeri, consentendo la definizione di diverse categorie per gli eventi. Le prestazioni statistiche di questa analisi sono caratterizzate da due parametri essenziali: i limiti superiori sulla signal strength e la significanza del segnale. I limiti attesi sulla signal strength sono stimati al 95% di livello di confidenza, assieme alla significanza del segnale, per ciascuna categoria e per la combinazione di tutte le categorie.

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I would like to express my sincere gratitude to Professor Andrea Castro, for his con-tinuous support throughout the thesis work and helpful advice. I wish to thank my family for the support and encouragement throughout my study.

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The Standard Model of Particle

Physics

The Standard Model (SM) of particle physics is the current description of the fundamen-tal constituents of our universe and interactions between them, developed as a result of a large amount of experimental and theoretical research. The model represents a milestone in the development of the most fundamental theory of matter and outlines the bound-aries of the present knowledge of particle physics, beyond which the region of new physics models begin. The aim of the SM has always been represented by providing an unified theoretical description of the three fundamental interactions which are dominant at the particle physics scales, the strong, weak and electromagnetic interactions, the last two being unified in a single Electroweak (EW) interaction.

In this chapter, the general framework of SM is outlined in Section 1.1 and a brief intro-duction of the elementary particles and their interactions is presented in Sections 1.2 and 1.3. A key concept of the SM is the Spontaneous Symmetry Breaking (SSB) of the EW sector which provides masses to the gauge bosons and matter fermions, reported in Sec-tion 1.4. Special attenSec-tion is reserved to the top quark and Higgs boson, both presented in Section 1.5, and their associated production, presented in Section 1.6.

1.1 General framework

The SM describes the structure of matter as consisting of elementary particles within

a spatial scale of 10 13 ₁₀ 17 _{cm, a scale so small to require a description based on}

the Quantum Field Theory (QFT) as general framework. The fields and particles are described by the generalized Lagrangian formalism, whose operators are dependent on the space-time point x. The Lagrangian density L is a functional of the fields (x) and

their space-time derivatives @µ , and its exact form is fixed by physical requirements

of the local gauge and relativistic invariance, and invariance with respect to groups of internal symmetry. Once the Lagrangian is fixed, the equations of motion are obtained by means of the action principle:

S = h Z d4xL( , @µ )

i

= 0. (1.1)

The theory has a gauge symmetry if there is a continuous group of local transformations of the fields (called gauge group) for which the action S remains unmodified. Since each continuous symmetry of L yields a conserved current and, hence, a conserved charge, the

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2 CHAPTER 1. THE STANDARD MODEL OF PARTICLE PHYSICS conservation laws are accounted for by symmetries of the Lagrangian density of the SM under gauge transformations of fields [1, 2, 3, 4].

1.2 Elementary particles

The most fundamental constituents of matter are referred to as elementary particles. They are grouped in two categories according to their spin numbers: fermions, which have half-integer spin, and bosons, which have integer spin.

1.2.1 Elementary fermions

Elementary fermions are further categorized into quarks and leptons.

• There are six quarks that are the constituents of the atomic matter. There are up (u), charm (c), top (t) quarks with electric charge of +2/3 and down (d), strange (s), bottom (b) with electric charge 1/3. Their charge, mass and spin are reported in Table 1.1 (values are taken from [5]).

Quark Electric Charge Mass Spin

u 2/3 2.16+0.490.26 MeV 1/2 d 1/3 4.67+0.48_0.17 MeV 1/2 c 2/3 1.27_{± 0.02 GeV} 1/2 s 1/3 93+115 MeV 1/2 t 2/3 172.9± 0.4 GeV 1/2 b 1/3 4.18+0.03_0.02 GeV 1/2

Table 1.1: Relevant physical properties of quarks.

• There are six leptons, three charged and three neutral fermions. Among the charged ones the electron (e) is the well known atomic particle, while the other two are the muon (µ) and the tau (⌧) that are heavier counterparts of the electron. The neutral

leptons are called neutrinos (⌫) and come in three generations ⌫e, ⌫µ, ⌫⌧. Their

charge, mass and spin are reported in Table 1.2.

Lepton Electric Charge Mass Spin

⌫e 0 < 2.05 eV (95% CL) 1/2 e 1 0.5109989461_{± 0.0000000031 MeV} 1/2 ⌫µ 0 < 0.19 MeV (90% CL) 1/2 µ 1 105.6583745_{± 0.0000024 MeV} 1/2 ⌫⌧ 0 < 18.2 MeV (95% CL) 1/2 ⌧ 1 1776.86_{± 0.12 MeV} 1/2

Table 1.2: Relevant physical properties of leptons.

1.2.2 Elementary bosons

Elementary bosons are the force carriers photon ( ), W±_{and Z bosons, gluons (g) and the}

mass-giving scalar particle, Higgs (H) boson. Their charge, mass and spin are reported in Table 1.3.

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1.3. INTERACTIONS 3

Boson Electric Charge Mass Spin

0 < 1 ⇥ 10 18_eV ₁ g 0 0 1 W+ ₁ _80.379_{± 0.012 GeV} ₁ W 1 80.379± 0.012 GeV 1 Z 0 91.1876_{± 0.0021 GeV} 1 H 0 125.10_{± 0.14 GeV} 0

Table 1.3: Relevant physical properties of bosons.

1.3 Interactions

Once these particles have been introduced, it is interesting to see how they interact with each other, through the electromagnetic, weak and strong forces. The corresponding theoretical parts of the SM are called Quantum Electrodynamics (QED), Quantum Fla-vordynamics (QFD) and Quantum Chromodynamics (QCD) and drafted in the following.

1.3.1 Electromagnetic interaction

All charged particles interact electromagnetically and the interaction is mediated by the photon as a gauge boson. The photon itself is neutral and does not directly interact with

itself. The free Lagrangian Lf ree of a fermion field , with mass m and charge q, is

invariant under U(1) transformations. It can be written as

Lf ree= ¯ (i µ@µ m) , (1.2)

where µ are the Dirac matrices. If we consider a global transformation, the complex

fermion field transforms as

(x)! ei↵_(x), _(1.3)

where ↵ is a real constant. The same invariance does not hold true under a local U(1)

transformation, U(x) = ei↵(x)Q_{, where ↵(x) is not a constant and it depends on}

space-time arbitrarily, and Q is the charge operator of the U(1) group. The term that actually breaks the invariance is the derivative of the fermion field, which transforms as

@µ ! ei↵(x)Q@µ + iei↵(x)Q @µ↵. (1.4)

In order to have an invariant Lagrangian under this transformation, the derivative must

be replaced by the covariant derivative, Dµ, which transforms covariantly like itself and

it introduces an addition vector field Aµ to cancel the invariance breaking terms in the

above equation Dµ = @µ ieQAµ, (1.5) where Aµ transforms: Aµ! Aµ+ 1 e@µ↵. (1.6)

The covariant derivative assures that the free Lagrangian remains invariant under local

transformations. This vector field, called the gauge boson Aµ, is the physical photon field.

Therefore adding the kinetic energy of the photon field (Fµ⌫ = @µA⌫ @⌫Aµ), which also

needs to be invariant under U(1), leads to the QED Lagrangian

LQED= ¯ (i µ@µ m) + eQ ¯ µAµ

1

4Fµ⌫F

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4 CHAPTER 1. THE STANDARD MODEL OF PARTICLE PHYSICS

A mass term such as 1

2m

2_A

µAµ would not be allowed in the free Lagrangian since it

would break the gauge invariance: as a consequence, the gauge field photon is massless.

1.3.2 Strong interaction

All particles with colour charge interact via strong interactions and are mediated by gluons. The strong interactions account for holding the proton and neutron together in an atom, as well for keeping the quarks confined in a hadron. A hadron is a composite particle made of quarks and antiquarks. The gluon itself has a colour charge, which allows for the appearance of self-interactions. None of the coloured particles, quarks and gluons, can be observed as a free particle and they are always confined in colourless states. This phenomenon is called colour confinement. Quarks come in three colours red (r), green (g) and blue (b), antiquarks with anti-colours ¯r, ¯g, ¯b, while gluons carry one unit of colour and one unit of anti-colour. Mesons are colour neutral states formed by quark-antiquark pairs (i.e. r¯r) while baryons are groups of three quarks (rgb), antibaryons are groups of three antiquarks (¯r¯g¯b). QCD is the theory of the strong interactions between quarks and

gluons and describes the SU(3)C colour symmetry (where C stands for colour). The free

Lagrangian is required to be invariant under the following SU(3) gauge transformation

q(x)_{! Uq(x) = e}i↵k(x)Tk_q(x), (1.8)

where q is the quark triplet denoting the three colour quark states and U is an arbitrary

3_{⇥ 3 unitary matrix representing the SU(3) transformation. T}k with k = 1, ..., 8 are

linearly independent traceless matrices and ↵k are the group parameters. The local

symmetry is restored by introducing the covariant derivative

Dµ= @µ+ igsTkGkµ, (1.9)

where gs is the strong coupling constant, Gkµ represents the eight gauge fields and

trans-forms in a more complicated way compared to the photon field

Gkµ! Gkµ

1

g@µ↵k fklm↵lG

m

µ, (1.10)

where fklmare the structure constants of the group which is diﬀerent from the QED case

due to the non-abelian structure of the SU(3) group. This leads to the self-interacting gluon terms in the Lagrangian which is also diﬀerent than the photon field. Adding the gauge invariant kinetic term for each of the gluon fields, the gauge invariant QCD Lagrangian becomes LQCD= ¯q(i µ@µ m)q g(¯q µTaq)Gaµ 1 4G a µ⌫Gµ⌫a . (1.11)

As in the case for U(1) gauge invariance, requiring the Lagrangian to be invariant under colour gauge transformations leads us to 8 self interacting massless gluon fields.

1.3.3 Weak interaction and Electroweak Unification

The weak interactions are mediated by the massive W± _{and Z vector bosons and they}

account for the well-known nuclear beta decay. Unlike the electromagnetic and strong interactions, only left-handed fermions and right-handed anti-fermions interact weakly. As a result, the chiral symmetry is broken suggesting that the gauge symmetry of the weak interactions is more complicated compared to the U(1) and SU(3) symmetries. In order to describe the weak interactions of fermions, the electromagnetic and weak interactions

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1.4. SPONTANEOUS SYMMETRY BREAKING AND THE BEH MECHANISM 5 are unified as electroweak interactions. The electroweak interaction is invariant under

the SU(2)L⇥ U(1)Y weak isospin and hypercharge symmetry, where L stands for left

and Y represents the weak hypercharge, defined as Q = I3+ Y₂, with I3 being the

third component of weak isospin. Left-handed fermions are grouped into doublets of

weak isospin I3 =±1/2 and right-handed fermions are isospin singlets with I3 = 0. In

SU(2)L⇥ U(1)Y the left-handed and right-handed fermions transform diﬀerently as

L! ei↵k(x)⌧k2+i (x)

Y

2L R! ei (x)

Y

2R, (1.12)

where ⌧k/2are the generators of weak isospin group SU(2)Lbuilt from the Pauli matrices

⌧k(with k = 1, 2, 3), Y/2 is the generator of the hypercharge group U(1) and R represents

the right-handed fermions. As in U(1) and SU(3) representations, we can introduce the

vector fields to ensure the gauge invariance: Wk

µ, with k=1,2,3, is introduced for the

SU(2)L and a single vector field Bµ for the U(1)Y. Then the covariant derivative is:

Dµ= @µ+ i g 2⌧kW k µ+ i g0 2 Y Bµ, (1.13)

with couplings g and g0 _{for the SU(2)}

L and U(1)Y respectively. The SU(2)L is a

non-abelian group, as SU(3), that the Wk vector fields transform similar to the gauge bosons

and the B vector fields. Adding the kinetic terms of the gauge bosons to the free La-grangian leads us to the electroweak LaLa-grangian

LEW K = i ¯L µDµL + i ¯R µDµ R 1 4W k µ⌫Wk,µ⌫ 1 4Bµ⌫B µ⌫_. _(1.14)

The electroweak Lagrangian is invariant with massless vector bosons, however it is known

that the W± _{and Z bosons are massive. The masses of the vector bosons need to be}

added in the theory ensuring the gauge invariance. This happens through the electroweak symmetry breaking mechanism, the so-called the Brout-Englert-Higgs (BEH) mechanism.

1.4 Spontaneous Symmetry Breaking and the BEH

mech-anism

So far, we have shown that the mass terms of the gauge bosons are not allowed in a gauge invariant theory. As a consequence massive gauge bosons will break the symmetry. In order to allow massive gauge bosons while keeping the Lagrangian invariant under the presented gauge symmetries, we need to introduce the SSB mechanism. The SSB is achieved by adding a scalar field to the Lagrangian, for which the non-zero vacuum expectation values (ground state) break the symmetry. The choice of the field for a SU(2) gauge symmetry is a doublet of complex scalar fields

= ✓ _†◆ = p1 2 ✓ 1_{+ i} 2 3_{+ i} 4 ◆ , (1.15)

and the SU(2) invariant Lagrangian is

L = (Dµ )†(Dµ ) V ( † ), (1.16)

where

V ( † ) = µ2 † _{+ (} † ₎2_, _(1.17)

and the covariant derivative defined in Eq. 1.13. There are two possible forms of this

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set at < >= 0. This represents a system of four scalar particles each with a mass µ

interacting with 3 massless gauge bosons Wk

µ and it does not break the symmetry. The

most interesting case is µ2_{< 0. The ground state minimum is given by}

† ₌ 1 2( 2 1+ 22+ 23+ 24) = µ2 2 . (1.18)

The ground state is associated to a vacuum expectation value v = ±qµ2

. The Lagrangian symmetry is broken by the choice of one of the ground states, it is either +v or v, where the Lagrangian is not symmetric. The field needs to conserve the U(1) symmetry and

breaks SU(2)L. Therefore the field can be fixed to a minimum energy position by choosing

1= 2= 4= 0and 23= µ

2

= v2 _{and can be parametrised by h(x) which represents}

the fluctuations of this minimum

= e⌧i✓i(x)/v_p1 2 ✓ 0 v + h(x) ◆ . (1.19)

Here h(x) is the BEH field, ⌧1,2,3are the generators of SU(2)L, and ✓1,2,3are the massless

Goldstone bosons. According to the Goldstone theorem, the spontaneously broken

sym-metry leads to massless scalars as many as the broken generators. The SU(2)L symmetry

allows to rotate away any dependence on ✓i(x). Choosing the unitarity gauge ✓i(x) = 0,

eliminates the ✓i fields in the Lagrangian so that Goldstone bosons are absorbed by the

three gauge bosons that require masses and give the longitudinal components to the mas-sive gauge bosons. The BEH potential of the SSB Lagrangian takes the following form

V ( † ) = 1 2(2 v 2_{) h(x)}2_{+ v h(x)}3₊ 4h(x) 4 4 v 4_. _(1.20)

The BEH potential has quadratic, cubic and quartic terms of the BEH field. The first term is the mass term of the BEH field

mH =

p

2 v =p2 |µ| (1.21)

and it depends on the self BEH coupling and the v. The cubic and quartic terms

correspond to self-interactions of the BEH field, and the last term is a constant. Inserting the new scalar field with the covariant derivative, it becomes

(Dµ )†(Dµ ) = 1 2|@µh(x)| 2₊1 8v 2_[g2_(W2 1 + W22) + (gW3 g0Bµ)2] +O(h(x)). (1.22)

Here the first term is the kinetic term of the BEH field while the last term has the interactions of the BEH field with the gauge boson. We will focus on the second term in the Lagrangian which gives the mass terms of the gauge bosons. We can rewrite this

term of the Lagrangian in terms of the known W±_{, Z and A bosons as}

1 8v 2_[g2_(W+ µ)2+ g2(Wµ)2+ (g2+ g02) Zµ2+ 0· A2µ], (1.23) where Wµ±= 1 p 2(W1± iW2), with MW±= 1 2vg Zµ= 1 p g2_{+ g}02(gW3 g 0_B µ), with MZ = 1 2v p (g2_{+ g}02₎ Aµ=p 1 g2_{+ g}02(g 0_W 3+ gBµ), with MA= 0 (1.24)

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1.4. SPONTANEOUS SYMMETRY BREAKING AND THE BEH MECHANISM 7 Also, the ratio of the W and Z boson masses is equal to the cosine of the weak mixing

angle ✓W

MW/MZ = g/

p

g2_{+ g}02 _{= cos(✓}_W_). _(1.25)

The weak mixing angle is a parameter of the SM that rotates the W3, Bµ vector boson

plane producing the Z and Aµ bosons by SSB. Additionally it relates the couplings as

e = g sin (✓W) = g0cos (✓W). (1.26)

The experimental measurements of MW, MZ and ✓W confirm the above relation, which

is typically written in the form

sin2(✓W) = 1 cos2(✓W) = 1 M 2 W M2 Z . (1.27)

The components containing fermion fields can be also expressed in terms of the angle

✓W and the fields Wµ±, Zµ and Aµ, leading to the neutral-current Lagrangian LN C and

charged-current Lagrangian LCC LN C= eJµAAµ+ g cos(✓W) JµZZµ, (1.28) LCC = g p 2(J + µW+ µ JµW µ), (1.29)

where the currents Jµ are given by

JµA= Qf ¯ µ , JµZ= 1 2 ¯ µ[(T 3 f 2Qfsin2(✓W)) 5(Tf3)] , Jµ+= 1 2u¯ µ(1 5) d, (1.30)

with u and d representing the up and down-type fermions, while refers to either of

them, and Qf is the electric charge of the fermion.

So far, using the gauge invariance of the theory, we showed how the W and Z bosons gain their mass while the photon remains massless with the addition of the BEH field. But we still need to discuss how fermions acquire their mass. We have shown how the fermion

fields transform under SU(2)L⇥ U(1)Y rotations. The mass terms of the fermions are

not allowed since left-handed fermions form an isospin doublet and right-handed fermions

form isospin singlets and terms like m[ ¯L R+ ¯R L]are not gauge invariant. Therefore

a singlet term of SU(2)L⇥ U(1)Y is needed for an invariant Lagrangian mass term. This

can be done by introducing the BEH doublet into the Lagrangian,

Lf ermions= f[ ¯L R+ ¯R L], (1.31)

for the electron this term becomes

e(v + h) p 2 [¯eLeR+ ¯eReL] = ev p 2ee¯ e p 2h¯ee (1.32)

where eL, eR refer to the left- and right-handed electrons. The first term gives the mass

term of the electron, ev/p2and the second term describes the interactions between the

BEH field and the fermions. The parameter is very important and describes the Yukawa coupling of a fermion to the BEH field and it is expressed as

f =

p

2mf

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8 CHAPTER 1. THE STANDARD MODEL OF PARTICLE PHYSICS which is proportional to the mass of the fermion and v ' 246 GeV. This mass term only gives mass to “down” type of leptons, while keeps the “up” type of leptons, neutrinos, massless. In fact, despite experimental evidence for neutrino oscillations, which implies non-zero neutrino masses, the SM does not predict non-zero masses for neutrinos in a natural way. In order to have mass terms for the up type quarks, an additional term is needed in the Lagrangian. This is done by introducing the charge-conjugate representa-tion of the BEH doublet, which under SU(2) rotarepresenta-tions transforms as the original BEH field ˜C₌ _i⌧ 2 ?= r 1 2 ✓ v + h 0 ◆ , (1.34)

where ˜C _{is the charge conjugate representation of the BEH doublet. The mass term of}

the up-type fermion becomes

Lup = q[¯uL˜CuR+ ¯uR˜CuL] (1.35)

where u represents the up-type fermions. This mass term has the same form as the down-type fermions with the corresponding Yukawa couplings. All the mass terms of the SM particles can be expressed in terms of the vacuum expectation value v and the coupling

constants: g, g0_,

i where the Yukawa couplings, i, are diﬀerent for each lepton and

quark, and zero for neutrinos in the SM. Finally, we can gather all the ingredients of the

SM, SU(3) ⇥ SU(2)L⇥ U(1)Y and summarize all the interaction and mass terms in the

Lagrangian LSM = 1 4Wµ⌫W µ⌫ 1 4Bµ⌫B µ⌫ 1 4Gµ⌫G µ⌫ | {z }

W±, Z, and gluon kinetic energies and self interactions

+ + `L µ(i@µ g 1 2⌧ i_Wi µ g0 Y 2Bµ)`L+ qL µ_(i@ µ g 1 2⌧ i_Wi µ g0 Y 2Bµ gsT k_Gk µ)qL | {z }

left handed fermion kinetic energies and their interactions

+ + `R µ(i@µ g0 Y 2Bµ)`R+ qR µ_(i@ µ g0 Y 2Bµ gsT k_Gk µ)qR | {z }

right handed fermion kinetic energies and their interactions

+ +|(i@µ g1 2⌧ i_Wi µ g0 Y 2Bµ) | 2 _{V (} † ₎ | {z }

W±,Z, and BEH masses and coupling

( f`¯L `R+ gq¯L˜CqR+ h.c.)

| {z }

fermion masses and couplings to BEH , (1.36) where ` is used for leptons and q for quarks.

1.5 Top quark and Higgs boson physics

The top quark and the Higgs boson are among the most recently discovered SM particles. Due to their large mass and their distinctive properties, they are of special interest to a large fraction of particle-physics analyses performed today. Most of the properties of the top quark and the Higgs boson are well known by now. An overview of them, together with the production and decay modes, is presented in the following. With the discovery of the Higgs boson, the last missing piece of the SM has been found.

1.5.1 Top quark

The top quark is the up-type quark of the third generation of elementary particles, with a mass of approximately 173 GeV. The top quark, together with its antiparticle, the

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1.5. TOP QUARK AND HIGGS BOSON PHYSICS 9 antitop quark, has been discovered in 1995 by the CDF and D0 experiments at the proton-antiproton collider Tevatron at the Fermilab laboratory [11, 12]. With its high mass, the top quark is particularly interesting for searches for Beyond the Standard Model (BSM) physics and precision measurements of its properties play a significant role at the ongoing physics schedule at the Large Hadron Collider (LHC) at CERN. Moreover, the top quark has other unique and special properties, such as the large value of its width

of about 1.35 GeV [5] that causes it to have a very short lifetime of about 5.0 ⇥ 10 25

s. This implies that the top quark decays before any hadronization can occur. This allows us to determine spin information transferred to its decay products undiluted by non-perturbative eﬀects.

Top quark production

The top quark can be produced in pairs through the strong interaction or singly through the weak interaction. The top quark-antiquark pair production (t¯t) is a pure QCD process and can be initiated in two diﬀerent ways, either by gluons or by a quark-antiquark pair in the initial state. Both types of t¯t production are illustrated by Feynman diagrams in

Fig. 1.1. At the LHC with a centre-of-mass energy ofps= 13 TeV, about 90% of the

Figure 1.1: Leading order Feynman diagrams for the top quark-antiquark pair production. top quarks are produced via the gluon-initiated process. Although the top quark pair production requires enough energy to produce two top quarks, it represents the main production mode at the LHC. This fact can be explained by the large coupling constant of the strong interaction.

Single top quarks are produced via the weak interaction. This process includes a ver-tex of a top quark, a W boson, and a down-type quark. The contribution of diﬀerent down-type quarks to this vertex is determined by the corresponding

Cabibbo-Kobayashi-Maskawa (CKM) matrix element. As the CKM matrix element Vtb is close to one and

the others negligibly small, the vertex includes a bottom quark in almost all cases. Cor-respondingly, the single top quark production is well suited for the measurement of the

CKM matrix element Vtb. The single top quark production is further subdivided into

three production modes: the t-channel, the associated production with a W boson (tW) and the s-channel. Feynman diagrams of the single top quark production are given in Fig. 1.2 ordered by their cross section at the LHC. Single top quark production features a cross section that is about five times smaller than top quark pair production at a centre-of-mass

energy ofps= 13 TeV.

Top quark decay

The top quark decays only through the weak interaction. It decays into a W boson and

a bottom quark in almost all of the cases, because of the large CKM matrix element Vtb.

One distinguishes between the leptonic and the hadronic decay of a top quark, which is characterised by the decay of the W boson. A leptonic decay of a top quark features a

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Figure 1.2: Leading order Feynman diagrams for single top quark production. From left to right: t-channel, tW, s-channel.

W-boson decay into a charged lepton and a neutrino. A hadronic decay of a top quark is indicated by a W boson decay into an up-type and a down-type quark and antiquark. A decay of the W boson into a final state featuring a top quark is not possible due to the large mass of the top quark. Accordingly, the hadronic W boson decay produces mainly quarks from the first and the second generation. Taking into account the three diﬀerent colour charges of quarks, the branching ratio for the hadronic top quark decay occurs twice as often as the leptonic decay. Transferring this categorisation to the decay of a top quark pair provides three diﬀerent configurations:

• Dileptonic t¯t decay channel: both top quarks decay leptonically. The dileptonic decay channel features a branching ratio of 10.5%.

• Semileptonic t¯t decay channel: one top quark decays leptonically, while the other top quark decays hadronically. The semileptonic decay channel features a branching ratio of 43.8%.

• All-hadronic t¯t decay channel: both top quarks decay hadronically. The all-hadronic decay channel features a branching ratio of 45.7%.

1.5.2 Higgs boson

The Higgs boson is a spin-zero particle resulting from the Higgs mechanism with a mass of approximately 125 GeV. Until its discovery in 2012 by ATLAS and CMS [7, 8], the Higgs boson has been the last missing piece of the SM. The discovery of a new resonance with and the subsequent studies of its properties have provided the first portrait of the BEH mechanism. The Higgs boson mass has been precisely measured and its production and decay rates are found to be consistent, within errors, with the SM predictions. In the following, a brief description of the Higgs boson couplings, production and decay modes is presented, followed by an overview of its discovery.

Higgs boson couplings

The Higgs boson couplings to the fundamental particles are determined by their masses: very weak for light particles, such as light quarks and electrons, but strong for heavy particles such as the W and Z bosons and the top quark. More precisely, the Higgs boson couplings to fermions and gauge bosons, as well as the Higgs boson self coupling, are summarized in the following Lagrangian:

LH= gHf ¯ff f H +¯ gHHH 6 H 3₊gHHHH 24 H 4₊ VVµVµ ⇣ gHV VH + gHHV V 2 H 2⌘ _(1.37)

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1.5. TOP QUARK AND HIGGS BOSON PHYSICS 11 with gHf ¯f = mf v , gHV V = 2m2 V v , gHHV V = 2m2 V v2 , gHHH = 3m2 H v , gHHHH= 3m2 H v2 . (1.38) It can be seen that the SM Higgs couplings to fundamental fermions are linearly pro-portional to the fermion masses, whereas the couplings to bosons are propro-portional to the square of the boson masses. It is also possible for the Higgs boson to self-interact. Higgs boson production

The Higgs boson can be produced in many ways at the LHC (Fig. 1.3). The main

Figure 1.3: Leading order Feynman diagrams for Higgs boson production. Gluon-gluon fusion (upper left), VBF (upper right), VH (lower left), t¯tH (lower right).

production mode at the LHC is the gluon-gluon fusion (ggH), featuring gluons in the initial state. As the Higgs boson does not couple to massless particles, the top quark is produced via intermediately generated particles in this process. Further, the intermediate particles can be only quarks and not gluons which only couple to colour charged particles. The largest contribution is provided by the top quark, due to its large mass and the resulting large coupling to the Higgs boson, as discussed. The main reason for the comparably large cross section is the large number of gluons in a proton-proton collisions with an energy suﬃcient to enter this process. Gluons carry a large fraction of proton momentum, as it is known from the parton distribution functions which describe the probability distributions for a parton carrying a particular momentum. The second-largest Higgs boson production mode is vector-boson fusion (VBF). This process starts with two quarks in the initial state, which produce virtual vector bosons. The vector bosons in turn produce a Higgs boson. The comparably large cross section can be explained by the large coupling of the Higgs boson to the vector bosons. A special characteristic of this process is the two outgoing quarks. The two quarks form two jets, which are directed in the forward direction of the detector. This special trait simplifies a targeted search for VBF. A further production mode is the associated production of a Higgs boson with a vector boson (VH). This process is also known as Higgs-strahlung, which refers to bremsstrahlung as analogue

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12 CHAPTER 1. THE STANDARD MODEL OF PARTICLE PHYSICS process. In the VH process, a vector boson is produced by the annihilation of a quark and an antiquark. The Higgs boson is radiated by the vector boson. VH production is the Higgs boson production mode with the third-largest cross section among all SM Higgs boson production modes. The associated production of a Higgs boson with a top quark pair (t¯tH) has the smallest cross section among the four main Higgs boson production modes. In this process, a top quark pair is produced as described in the previous section. The Higgs boson is radiated from one of the top quarks. Even though the coupling of the Higgs boson to the top quark is comparably strong, t¯tH production features a very small cross section. This is mainly due to the enormous amount of energy of about 500 GeV necessary to produce these three massive particles.

Higgs boson decay

The Higgs boson can decay in different channels governed by branching ratios, which are reported in Table 1.4 (values from [5]). The masses of the Higgs boson and of the decay products are the main factors determining the branching ratios. A decay into top quarks, which would be favoured due to the coupling, is not possible as the mass of two top quarks largely exceeds the mass of the Higgs boson. Instead, the largest branching ratio is provided by the Higgs boson decay into two bottom quarks. This decay makes up almost 60% of all Higgs boson decays. However, a search for Higgs bosons decaying into a bottom quark pair at the LHC is challenging due to the large background from QCD processes. The second largest contribution with a branching ratio of about 20% is given by the Higgs boson decay into two W bosons, where one W boson is produced off-shell. In case of the W bosons decaying into leptons, this decay provides a very clean signature. One of the search channels mainly contributing to the Higgs boson discovery in 2012 is based on the Higgs boson decay into two Z bosons. If the Z bosons decay into charged leptons, this decay channel provides a very distinctive signature as there are hardly any backgrounds featuring four charged leptons. Due to the good momentum resolution of charged leptons, a very narrow Higgs boson mass peak can be reconstructed in this search channel. Again, one of the bosons is produced off the mass shell as the invariant mass of two Z bosons exceeds the Higgs boson mass. The second Higgs boson decay mode with a major contribution to the Higgs boson discovery is the decay into two photons. As for the gluons in the Higgs boson production by gluon fusion, the massless photons do not couple to the Higgs boson directly. Instead, this decay proceeds via a loop. Compared to gluon fusion, all electrically charged massive particles may contribute to the loop. Accordingly, a further major contribution is given by the W boson. The Higgs boson decay into two photons also features a very clean final state with a very good Higgs boson mass resolution. However, this decay channel has a very small branching ratio compared to the other Higgs boson decay modes described.

Decay channel Branching ratio Rel. uncertainty

H_{! b¯b} 58.4% +3.2%_3.3% H! W+_W _21.4% +4.3% 4.2% H_{! ⌧}+_⌧ _6.3% +5.7% 5.7% H_{! Z Z}⇤ _2.62% +4.3% 4.1% H_! 0.23% +5.0% 4.9% H_{! Z} 0.15% +9.0%_8.9% H! µµ 0.02% +6.0% 5.9%

Table 1.4: Decay channels and branching ratios for a SM Higgs boson with mH = 125

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1.5. TOP QUARK AND HIGGS BOSON PHYSICS 13 In the SM, the Higgs boson width is very precisely predicted once the Higgs boson mass is known. For a mass of 125 GeV, the Higgs boson has a very narrow width of 4.2 MeV. The total width is dominated by the fermionic decays at approximately 75%, while the vector boson modes are suppressed and contribute 25% only. Explicitly, the partial widths are given by the relations

(H! f ¯f ) = GFm 2 fmHNc 4⇡p2 ⇣ 1 4m2f/m2H ⌘3/2 (1.39) (H _{! W}+W ) = GFm 3 H W 32⇡p2 ⇣ 4 4aW + 3a2W ⌘ (1.40) (H _{! ZZ) =} GFm 3 H Z 64⇡p2 ⇣ 4 4aZ+ 3a2Z ⌘ (1.41)

where Nc is 3 for quarks and 1 for leptons and where aW = 1 W2 = 4m2W/m2H and

aZ = 1 Z2 = 4m2Z/m2H. The decay to two gluons proceeds through quarks loops and

the partial width is given by the relation

(H_{! gg) =} ↵ 2 SGFm3H 36⇡3p₂ X q I(m2 q/m2H) 2 (1.42)

where I(z) is complex for z < 1/4. For z < 2 ⇥ 10 3_{, I(z) is small so the light quarks}

contribute negligibly. For mH < 2mt, z > 1/4 and

I(z) = 3h2z + 2z(1 4z)⇣sin 1 1

2pz

⌘2i

(1.43) which has the limit I(z) ! 1 as z ! 1.

Higgs boson observation

In 2012, the Higgs boson has been independently observed by the ATLAS and CMS collaborations [7, 8]. The announcement on July 4, 2012, of the observation at the LHC of a narrow resonance with a mass of about 125 GeV was an important landmark in the decades-long direct search [13, 14] for the SM Higgs boson. This was followed by a detailed exploration of properties of the Higgs boson at the diﬀerent runs of the LHC at

p_s_{= 8 and 13 TeV. For this discovery, various searches targeting diﬀerent Higgs boson}

decay channels have been combined. For a given value of the Higgs boson mass mH, the

sensitivity of a search channel depends on the production cross section of the Higgs boson, its decay branching fraction, reconstructed mass resolution, selection eﬃciency and the

level of background in the final state. For a low-mass Higgs boson (110 GeV < mH < 150

GeV) where the natural width is only a few MeV, five decay channels play an important

role at the LHC. In the H ! and H ! ZZ ! 4` channels, all final state particles can

be very precisely measured and the reconstructed mH resolution is excellent (typically 1

2%). While the H ! W+_W _{! `}+_{⌫` ¯}_⌫ _{channel has relatively large branching fraction,}

the mH resolution is poor (approximately 20%) due to the presence of neutrinos. The

H! b¯b and the H ! ⌧+_⌧ _{channels suﬀer from large backgrounds and an intermediate}

mass resolution of about 10% and 15% respectively. For mH > 150 GeV, the sensitive

search channels were H ! WW and H ! ZZ where the W or Z boson decays into a variety of leptonic and hadronic final states. The candidate events in each Higgs boson decay channel are split into several mutually exclusive categories based on the specific topological, kinematic or other features present in the event. The categorisation of events

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14 CHAPTER 1. THE STANDARD MODEL OF PARTICLE PHYSICS increases the sensitivity of the overall analysis and allows a separation of diﬀerent Higgs boson production processes. In the following, a brief summary of the observation of Higgs

boson decay into a pair or into a ZZ⇤ _{is presented.}

In the H ! channel, a search is performed for a narrow peak over a smoothly falling

background in the invariant mass distribution of two high-pT photons. The background in

this channel is conspicuous and stems from prompt diphoton processes for the irreducible backgrounds, and the +jet and dijet processes for the reducible backgrounds where one

jet fragments typically into a leading ⇡0_{. In order to optimise search sensitivity and also to}

separate the various Higgs production modes, ATLAS and CMS experiments split events

into several mutually exclusive categories. Diphoton events containing a high-pT muon

or electron, or missing transverse energy (Emiss) consistent with the decay of a W or Z

boson are tagged in the VH production category. Diphoton events containing energetic dijets with a large mass and pseudorapidity diﬀerence are assigned to the VBF production category, and the remaining events are considered either in the VH category when the two jets are compatible with the hadronic decay of a W or a Z, or in the gluon-fusion production category. While the leptonic VH category is relatively pure, the VBF category has significant contamination from the gluon fusion process. Events which are not picked by any of the above selections are further categorised according to their expected m

resolution and signal-over-background ratio. Categories with good mH resolution and

larger signal-over-background ratio contribute most to the sensitivity of the search. The

m distribution after combining all categories is shown for the ATLAS experiment in

Fig. 1.4 (left) using Run 2 data. The signal strength µ = ( · BR)obs/( · BR)SM in

the diphoton decay of the Higgs boson is 1.17 ± 0.27 for ATLAS in Run 1 [15] and 0.99 ± 0.14 [16] in Run 2. The signal strengths measured in Run 1 and Run 2 by the CMS

collaboration are 0.78+0.26

0.23 [17] and 1.16+0.150.14 [18] respectively.

In the H ! ZZ⇤_{! 4` channel, a search is performed for a narrow mass peak over a small}

Figure 1.4: (Left) The invariant mass distribution of diphoton candidates, with each event weighted by the signal-over-background ratio in each event category, observed by ATLAS at Run 2. The residuals of the data with respect to the fitted background are displayed

in the lower panel. (Right) The m4`distribution from CMS Run 2 data.

continuous background dominated by non-resonant ZZ⇤_{production from q¯q annihilation}

and gg fusion processes. The contribution and the shape of this irreducible background are taken from simulation. The subdominant and reducible backgrounds are derived

from data. To help distinguish the Higgs signal from the dominant non-resonant ZZ⇤

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1.6. HIGGS BOSON PRODUCTION IN ASSOCIATION WITH A TOP QUARK PAIR15 a kinematic discriminant built for each 4` event. To further enhance the sensitivity of a signal, various techniques based on the matrix element or the multivariate analysis are

used by the experiments. Since the m4` resolutions and the reducible background levels

are diﬀerent in the 4µ, 4e and 2e2µ subchannels, they are analysed separately and the results are then combined. The distribution of the reconstructed invariant mass of the four leptons for the CMS experiment is given in Fig. 1.4 (right), showing a clear excess at a

mass of approximately mH= 125 GeV. Both experiments also observe a clear peak at m4`

= 91 GeV from the production of a Z boson on-mass-shell and decaying to four leptons due typically to the emission of an oﬀ-shell photon from one of the primary leptons from the Z boson decay. The signal strengths µ for the inclusive H ! 4` production measured by

the ATLAS and CMS experiments are 1.44+0.40

0.33 [19] at mH = 125.36 GeV and 0.93+0.290.25

[20] at mH = 125.6 GeV respectively, in Run 1. The signal strengths measured by the

ATLAS and CMS experiments in Run 2 are 1.28+0.21

0.19 [21] and 1.05

+0.19

0.25 [22] respectively,

both measurements are made at the combined Run 1 Higgs mass of mH = 125.09 GeV.

1.6 Higgs boson production in association with a top

quark pair

The Higgs boson produced in association with a top quark-antiquark pair (t¯tH) is a very interesting channel and represents the subject of this thesis. A special characteristic of

t¯tH production is to give direct access to the coupling of the Higgs boson to the top

quark, the so-called top quark Yukawa coupling. However, the experimental observation of this process is complicated due to its small cross section and an overwhelming amount of background. Substantial indirect evidence of this coupling is provided by the compati-bility of observed rates of the Higgs boson produced through gluon fusion involving a top quark loop in the principal discovery decay channels. Direct evidence of this coupling at the LHC is available through t¯tH production which allows a clean measurement of the top quark with the Higgs boson coupling. In fact, according to the SM, the masses of ele-mentary fermions are accounted for by introducing a minimal set of Yukawa interactions, compatible with gauge invariance, between the Higgs and fermion fields. Following the spontaneous breaking of electroweak symmetry, charged fermions of flavour f couple to

H with a strength proportional to the mass of those fermions mf. Measurements of the

Higgs boson decay rates to down-type fermions (⌧ leptons and bottom quarks) agree with the SM predictions within their uncertainties. However, the top quark Yukawa coupling cannot be similarly tested from the measurement of a decay rate since on-shell top quarks are too heavy to be produced in Higgs boson decay. Instead, constraints on the coupling can be obtained through measurement of the t¯tH production process. The Feynman di-agram for t¯tH production is represented in Fig. 1.5, with the hadronic decay of the two top quarks and the Higgs boson.

1.6.1 Theoretical motivations for measuring t¯tH production

There are several motivations for studying the t¯tH production:

• The Higgs boson production mode in association with top quarks provides access

to a direct measurement of the top quark Yukawa coupling tto the Higgs boson.

Precise measurement of the Yukawa couplings of the Higgs boson to fermions f,

in general, remains a very important goal of the LHC, with the Yukawa interac-tion predicted to be the source of fermion masses. Any deviainterac-tions found between

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Figure 1.5: Feynman diagram for t¯tH production in the fully hadronic decay.

mf = fv₂ would be strong evidence for new physics. The top quark plays a key

role, being the heaviest SM particle whose predicted value of t' 1, with the latest

experimental measurement of 1.07+0.34

0.43 [23] with an upper limit of 1.67 at the 95%

confidence level in good agreement with the SM prediction. In comparison to the couplings of the Higgs boson to other fermions, it is almost two orders of magnitude

higher than the next largest coupling, b.

Measurements of tcan be extracted from processes involving loop eﬀects, such as

the gluon-fusion production. However, these channels only provide an indirect mea-surement where the top quark mediates the interactions in the loops and assumes no BSM eﬀects. Instead, the top-Higgs vertex present in t¯tH production provides

a direct measurement of t, significantly reducing the model dependence. A direct

measurement of thelps to constrain BSM searches and represents a precision test

of the SM consistency. Measurements from direct and indirect searches can also be compared, which would probe the presence of BSM particles mediating loops in indirect processes.

• The top quark Yukawa coupling also provides a window into the scale of new physics.

The eﬀective potential of the Higgs field is extremely sensitive to t. Small changes

in tcan modify the eﬀective potential from a monotonic behaviour which appears

as an extra minimum at very large values of the Higgs field [24].

In the absence of BSM signals the only way to address the question of the scale of new physics is to define the energy where the SM becomes theoretically inconsistent or contradicts some observations. Since the SM is a renormalisable quantum field theory, the problems can appear because of the renormalisation evolution of some coupling constants, i.e. when they become large (and the model enters strong cou-pling at that scale), or additional minima of the eﬀective potential develop changing the vacuum structure. The most dangerous constant turns out to be the Higgs

bo-son self-coupling constant with the renormalisation group (RG) evolution at one

loop. 16⇡ d d ln µ = 24 2_{+ 12} 2 t 9 (g2+ 1 3g 02₎ ₆ 4 t+ 9 8g 4₊3 8g 04₊3 4g 2_g02 _(1.44)

The right-hand side depends on the interplay between the positive contributions of the bosons and negative contribution from the top quark. The contribution of

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1.6. HIGGS BOSON PRODUCTION IN ASSOCIATION WITH A TOP QUARK PAIR17 the top quark to the eﬀective potential is very important, as it has the largest Yukawa coupling to the Higgs boson. Moreover, it comes with the minus sign and is responsible for the appearance of the extra minimum of the eﬀective potential at

large values of the Higgs field. In general, t should not exceed the critical value

crit, coinciding with good precision with the requirement of the stability of the

electroweak vacuum. To find the numerical value of crit, one should compute the

eﬀective potential for the Higgs field V ( ) and determine the parameters at which it has two degenerate minima:

V ( SM) = V ( 1) V0( SM) = V0( 1) = 0 (1.45)

The renormalization group eﬀective potential has the form:

V ( )/ ( ) 4h_{1 +}

O⇣ ↵_4⇡log(Mi/Mj)

⌘i

(1.46)

where ↵ is the common name for the SM coupling constants, and Mi,jare the masses

of diﬀerent particles in the background of the Higgs field. For t< crit 1.2⇥10 6

the eﬀective potential increases while the Higgs field increases, for t> crit 1.2⇥

10 6_{a new minimum of the eﬀective potential develops at large values of the Higgs}

field, at t= crit our electroweak vacuum is degenerate with the new one, while

at t > crit the new minimum is deeper than ours, meaning that our vacuum is

metastable. If t> crit+0.04the life-time of our vacuum is smaller than the age of

the Universe. The case t< crit 1.2⇥ 10 6is certainly the most cosmologically

safe, as our electroweak vacuum is unique. However, if t> crit 1.2⇥ 10 6 the

evolution of the Universe should lead the system to our vacuum rather than to the vacuum with large Higgs field (as far as our vacuum is the global minimum). While

in the interval t< crit 1.2⇥10 6< y < critour vacuum is deeper than another

one, in contrast with the case y > crit, where it is the other way around.

Variation of the top quark Yukawa coupling in the allowed by experimental and theoretical uncertainties interval changes the place where the scalar self-coupling

crosses zero from 107 _{GeV to infinity, without a clear indication of the necessity of}

new thresholds in particle physics between the Fermi and Planck scales. For the

largest allowed top Yukawa coupling the scale µnewis as small as 107GeV, whereas if

the uncertainties are pushed in the other direction no new physics would be needed below the Planck mass.

• Also, the t¯tH production has a very important role in the Eﬀective Field Theories (EFT) that study new physics through precise measurements of the production cross section of some processes like the t¯tH. In principle, an EFT is a low-energy approximation for a more fundamental theory involving particles of mass scale ⇤.

In practice, an EFT is based on the construction of an eﬀective Lagrangian Lef f by

adding new physics terms to the SM Lagrangian LSM that have dimension higher

than five, respecting the symmetries and conservation laws observed in nature,

Lef f =LSM+ X i c(6)i ⇤2O (6) i +O(⇤ 4_{) .} _(1.47)

The additional terms Oi are the operators constructed from the products of only

SM fields weighed by the Wilson coeﬃcients ci. The greater the dimension of an

operator, the more suppressed the corresponding factor, therefore operators of the lowest possible dimension are the most responsible for describing new physics (NP). For this reason, it is common practice to look with 6th order terms, avoiding the

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18 CHAPTER 1. THE STANDARD MODEL OF PARTICLE PHYSICS higher dimensions which are suppressed by the increasing 1/⇤ power.

The common EFT analysis strategy is to measure the cross section for a specific physics process and unfold this measurement back to the particle level, then make a comparison with EFT predictions [25]. Deviations from the SM prediction of the cross section are then included in the context of EFT through Wilson coeﬃcients.

In this case, for every operator, terms Mi will be added to the matrix element M

of a process:

M = M0+

X i

ciMi (1.48)

In the simplest case of a single added operator the cross section is then:

SM +N P(c)/ |M|2= s0+ s1ci+ s2c2i (1.49)

where s0 = SM, and s1 and s2 parametrise the cross section in terms of Wilson

coeﬃcient. The cross section has a quadratic dependence on the Wilson coeﬃcient of the added operator. Notice that the cross section does not necessarily reach its

minimal value when ci = 0. While in most cases the cross section is increased by

adding an operator, it is possible for the cross section to decrease owing to the partial cancellation with SM terms. According to the EFT, assuming baryon and lepton number conservation, there is a total of fifty-nine independent dimension-six operators [26], thirty-nine of those operators including at least one Higgs field. In the t¯tH production there are two kinds of relevant operators: those with four fermion fields and those with two or no fermion fields [27]. Considering the second kind, three operators can be defined:

Ot = y3t ⇣ † ⌘_{( ¯}_{Qt) ˜,} _(1.50) O G= yt2 ⇣ † ⌘_GA µ⌫GAµ⌫, (1.51) OtG= ytgs ⇣ ¯ Q µ⌫TAt⌘˜GAµ⌫. (1.52)

All three operators contribute to the t¯tH process at the tree level. The first one rescales the top quark Yukawa coupling in the SM, and also gives rise to a new ttHH coupling which contributes to Higgs pair production. The second one is a loop-induced interaction between the gluon and Higgs fields. Even though it does not involve a top-quark field explicitly, it is generally included for consistency because

the OtGmixes into this operator, and this operator in addition mixes into Ot . The

third one represents the chromo-dipole moment of the top quark. It modifies the gtt vertex in the SM and produces new four-point vertices, ggtt and gttH, as well as a five-point ggttH vertex. One can obtain the differential distributions at LO and NLO for the pp ! t¯tH process using the MG5_aMC generator [28] framework. As an example, it is reported in Fig. 1.6 the normalised differential cross section distribution as a function of the transverse momentum distributions of the t¯t system. The SM contribution as well as the individual operator contributions, normalised, are displayed, in order to compare the kinematic features from different operators. The magnitudes can be read off from the total cross section tables. In the lower panel the differential K factors are represented for each operator, together with the

µR,F uncertainties. Both interference and squared contributions are shown. Given

the current limits on the coeﬃcients, it is likely that the OtG operator still leads to

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1.6. HIGGS BOSON PRODUCTION IN ASSOCIATION WITH A TOP QUARK PAIR19

Figure 1.6: Normalised diﬀerential cross section distribution as a function of the transverse momentum distributions of the t¯t system

1.6.2 Observation of t¯tH production

Before the t¯tH observation took place, the CMS experiment had already performed sev-eral searches for t¯tH production using 7 and 8 TeV collision data from 2011 and 2012,

corresponding to 5 fb 1_{and 19.5 fb} 1_{, respectively [29, 30]. Searches at a centre-of-mass}

energy of 13 TeV have been conducted in the W+_W _{/multilepton, ZZ,} _{and ⌧⌧ final}

states of the Higgs boson with 35.9 fb 1_{of data collected in 2016 [31, 32, 33].}

The t¯tH production has been observed only recently in 2018 by the ATLAS and CMS Collaborations [34, 35]. This was the result of statistically independent searches for t¯tH decaying in diﬀerent topologies that were combined together to maximize sensitivity. In

the H ! channel, t¯tH events are searched for a narrow mass peak in the m

distri-bution. The background is estimated from the m sidebands. The sensitivity in this

channel is mostly limited by the available sample size. The H ! ZZ⇤_{! 4` channel is}

cur-rently limited by the low yields because of the small branching fraction of the Z decays to leptons. The H ! b¯b channel is intricate because of the large backgrounds, both physical and combinatorial in resolving the b¯b system from the Higgs decay, in events with six jets and four b-tagged jets. Already with the Run 1 dataset, the sensitivity of this analysis is strongly impacted by the systematic uncertainties on the background predictions. In this

thesis, special care is reserved for this channel. The channel H ! ⌧+_⌧ _{, where the two ⌧}

leptons decay to hadrons, has been also considered. Finally, the W+_{W , ⌧}+_{⌧ , and ZZ}⇤

final states can be searched for inclusively in multilepton event topologies. The signal over-background-ratio is displayed in Fig. 1.7. The presence of a t¯tH signal is assessed by performing a simultaneous fit to the data from the diﬀerent decay modes. The test statistic q, defined as the negative of twice the logarithm of the profile likelihood ratio, has been adopted, with the systematic uncertainties incorporated through the use of nuisance parameters treated according to the frequentist paradigm [36]. An excess of events from

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Figure 1.7: Signal-over-background ratio for ATLAS (left) and CMS (right). the SM for a Higgs boson mass of 125.09 GeV is observed, with an observed (expected) significance of 5.2 (4.2) standard deviations for the CMS collaboration, as can be seen in Fig. 1.8, and an observed (expected) significance of 6.3 (5.1) standard deviations for

the ATLAS collaboration. The combined (7+8+13 TeV) best-fit signal strength µt¯tH,

Figure 1.8: Test statistic q as a function of µt¯tH for all decay modes at 7 + 8 TeV and

at 13 TeV, shown separately and combined. The horizontal dashed lines indicate the p values for the background-only hypothesis obtained from the asymptotic distribution of q, expressed in units of the number of standard deviations.

defined as the observed t¯tH cross section t¯tH normalized to its the SM prediction t¯SMtH,

is 1.32+0.28

0.26(tot)for ATLAS and 1.26

+0.31

0.26(tot)for CMS (see Fig. 1.9).

In addition to comprising the first observation of a new Higgs boson production mech-anism, this measurement establishes the tree-level coupling of the Higgs boson to the top quark, and hence to an up-type quark, and is another milestone towards the measurement of the Higgs boson coupling to fermions. Also, the overall agreement observed between

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1.6. HIGGS BOSON PRODUCTION IN ASSOCIATION WITH A TOP QUARK PAIR21

Figure 1.9: Signal strengths for ATLAS (left) and CMS (right).

the SM predictions and data for the rate of Higgs boson production through gluon-gluon fusion decay mode suggested that the Higgs boson coupling to top quarks is SM-like, since the quantum loops in these processes include top quarks. However, non-SM particles in the loops could introduce terms that compensate for, and thus mask, other deviations from the SM. A measurement of the production rate of the tree-level t¯tH process provides clearer evidence for, or against, such new-physics contributions.

1.6.3 Theoretical cross section t¯tH production

The computation for the LO t¯tH cross section is very complicated and must take into consideration all the possible Feynman diagrams, displayed in Fig 1.10. The complete analytical expression for the LO gg ! t¯tH considers the all possibles permutation of exchanging the fermion with the antifermion and the gluons with each other from the Feynman diagram initiated by gluons (b), (c), (d). Following the notation of [37], we begin by denoting the four-momenta of the incoming gluons, top quark, top antiquark

and Higgs boson respectively by g1, g2, p, ¯p and k, and the gluon polarisation

four-vectors as ✏1 and ✏2. The invariant mass squared of the initial gluons is given by ˆs =

Q2= (g1+ g2)2= (p + ¯p + k)2 and the LO scattering amplitudes for the three diagrams

shown in (b), (c) and (d), labelled M1, M2 and M3, respectively, are given by:

M1= AXikaXkjb u¯j(p) k + p + mt 2p_{· k + M}2 H ✏2 ¯ p + g1+ mt 2g1· ¯p ✏1vi(¯p) + 8 > < > : g1$ g2, ✏1$ ✏2 g1$ g2, ✏1$ ✏2, p$ ¯p p$ ¯p 9 > = > ; (1.53) M2= AXikaXkjb u¯j(p)✏2p g2+ mt p_{· g}2 ¯ p + g1+ mt g1· ¯p ✏1vi(¯p) + g1$ g2, ✏1$ ✏2 (1.54) M3= iAfabcXijcu¯j(p) ✏1✏2Q ˆ s + h 2g⌫1g µ+(g2 g1) gµ⌫ 2g2µg⌫ i ¯p+ k mt 2k_{· ¯p + M}2 H vi(¯p)+ p! ¯p (1.55)

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(a) (b)

(c) (d)

Figure 1.10: Examples of LO Feynman diagrams for t¯tH production: (a) initiated by quarks; (b) initiated by gluons with t-channel exchange and radiation from external lines (c) initiated by gluons with t-channel exchange and radiation from internal lines; (d) initiated by gluons with s-channel exchange and radiation from external lines.

where A = 4⇡↵S(p2m2tGF)1/2are the coupling factors, and the SU(3) generators Xa

and structure constants fabc_{. The polarisation vectors obey the transversality condition}

✏i· gi = 0 and the SU(3) gauge invariance implies ✏1· g2 = ✏2· g1 and the invariance

substitutions ✏i$ gi.

The amplitude squared needs to be summed over the colour and spin states of the final quarks, and averaged over the colour and polarisation states of the initial gluons:

|M|2₌ 1

256 X spin,col

|M1+M2+M3|2. (1.56)

The trace over the matrices and the sum over the indices of the generators and

structure function yields:

(XikaXkjb )2= 24, (fabcXijc)2= 12, (XikaXkjb )(fabcXijc) = 0, (1.57)

while the average over the gluon polarisation states must be performed in an axial gauge (since the gluons are massless), for example:

2 X i=1 ✏µi(gi, i)✏i⌫(gi, i) = gµ⌫+ 2 ˆ s(g µ 1g2⌫+ g1⌫g µ 2) (1.58)

The cross section for the core gg ! t¯tH process is then obtained by integrating over the phase space as:

ˆLO = 1 ˆ s ↵2 SGFm2t p 2⇡3_(2⇡)9 Z _d3_p 2Et d3_p_¯ 2Et¯ d3_k 2EH (4)_(Q _p _p_¯ _k) |M|2 _(1.59)

The parton level cross section must then be folded with the gluon luminosity to obtain the full cross section for the process pp ! gg ! t¯tH:

LO= Z 1 0 1 2 h g(x1, µF) g(x2, µF) ˆLO(x1, x2, µF) + x1! x2 idx1dx2 (1.60)

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1.6. HIGGS BOSON PRODUCTION IN ASSOCIATION WITH A TOP QUARK PAIR23 Then we should consider the top quark and Higgs boson decays. The scattering amplitude must be multiplied by the decay amplitudes to give:

|Mgg!t¯tH!qqb,qqb,bb|2=|M|2· |Mt!qqb|2· |M¯t!qqb|2· |MH!b¯b|2. (1.61)

The top quark and Higgs boson decay amplitudes can be simplified with the narrow width approximation and expressed in terms of the vertex amplitudes:

The phase space must now only include the final state quarks. Denoting the four-momenta

of the top quark decay products as q1, q01, b1, those of the top antiquark as q2, q20, b2 and

those of the Higgs boson as b, ¯b, the phase space volume is parameterised as:

d = 1 (2⇡)24 d~q1 2Eq1 d~q0 1 2Eq01 d~b1 2Eb2 d~q2 2Eq1 d~q0 2 2Eq02 d~b2 2Eb2 d~b 2Eb d~b 2E¯_b (1.64)

The cross section for the gluon initiated t¯tH process in the all-hadronic decay channel is therefore given by:

gg!t¯tH!8q LO = 1 ˆ s ↵2 SGFm2t p 2⇡3 Z d (4)_(Q 8 X i=1 pi)|Mgg!t¯tH!qqb,qqb,bb|2 (1.65)

and the final cross section starting from protons is expressed as: pp!t¯tH!8q LO = Z 1 0 1 2 h g(x1, µF)g(x2, µF) LOgg!t¯tH!8q+ x1$ x2 idx1dx2 (1.66)

Values of the t¯tH production cross section as a function of the center of mass energy

p_s_{are reported in Table 1.5. For our analysis, which is a simulation at} p_{s = 13} _TeV,

the t¯tH cross section is 0.50+9%

13% (pb).

p_s _t¯tH_{production cross section (in pb)}

1.96 0.004+10%_10%

7 0.09+8%_14%

8 0.13+8%_13%

13 0.50+9%_13%

14 0.60+9%_13%

Table 1.5: SM Higgs boson production cross sections for mH= 125 GeV in pp collisions

(p¯p collisions atps = 1.96TeV for the Tevatron), as a function ofps. Values are taken

from [5].

1.6.4 The all-hadronic t¯tH channel

In the all-hadronic t¯tH decay mode channel, the Higgs boson decays exclusively to b¯b, and each top quark decays to a bottom quark and a W boson, which in turn decays to two quarks. Searches in which the H ! b¯b decay mode is selected and the W bosons are allowed to decay into leptons have also been reported by ATLAS [38] and CMS [39].

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ATLAS dedicated a search for t¯tH production in the all-hadronic final state atps= 8 TeV,

in which the observed and expected upper limits on the signal strength resulted to be 6.4

and 5.4 at 95% CL, and a best fit value for the signal strength of ˆµ = / SM = 1.6± 2.6

[40]. Six independent analysis regions are considered for the fit used by the ATLAS

analysis: two control regions (6j, 3b), (6j, 4b) and four signal regions (7j, 3b), (7j,

4b), ( 8j, 3b) and ( 8j, 4b). In addition, the three regions with exactly two

b-tagged jets, (6j, 2b), (7j, 2b) and ( 8j, 2b), are used to predict the multijet contribution to higher b-tagging multiplicity regions, using the tag rate function for multijet events (TRFMJ) method. The categories are analysed separately and combined statistically to maximise the overall sensitivity. The most sensitive regions, ( 8j, 3b) and ( 8j, 4b), are expected to contribute more than 50% of the total significance. The combined post-fit event yields for data, total background and signal expectations as a function of

log₁₀(S/B)are shown in the left panel of Fig. 1.11. The signal is normalised to the fitted

value of the signal strength (µ = 1.6). A signal strength 6.4 times larger than predicted by the SM is also shown in the left panel of Fig. 1.11. The all-hadronic best fit value

of ˆµ = / SM = 1.6± 2.6 has been combined with other t¯tH search channels in which

H_{! b¯b, and the combined result yields a best fit value of ˆµ = /} SM = 1.4± 1.0, as

shown in the right panel of Fig. 1.11.

Figure 1.11: (Left) Event yields as a function of log10(S/B)taken from the corresponding

BDT discriminant bin. The t¯tH signal is shown both for the best-fit value (µ = 1.6) and for the upper limit at 95% CL (µ = 6.4). (Right) Measurements of the signal strength for the t¯tH production in the H ! b¯b decay mode channels and their combination, assuming

mH = 125GeV. The SM µ = 1 expectation is shown as the grey line.

CMS published a search for t¯tH production in the all-hadronic decay channel atps =

13 TeV, corresponding to an integrated luminosity of 35.9 fb 1 _{[41]. Events, which are}

selected to be compatible with the H ! b¯b decay and the all-jet final state of the t¯t pair, are divided into six categories according to their reconstructed jet and b jet multiplicities:

(7j, 3b), (7j, 4b), (8j, 3b), (8j, 4b), ( 9j, 3b), ( 9j, 4b). Events 7j and 2b

are used to form control regions for the multijet background estimation. The categories are analysed separately and combined statistically to maximise the overall sensitivity.